programming-examples/java/Data_Structures/MaxMatchingHopcroftKarp.java

import java.util.*;
import java.util.stream.Stream;

// https://en.wikipedia.org/wiki/Hopcroft–Karp_algorithm in (E * sqrt(V))
public class MaxMatchingHopcroftKarp {

	public static int maxMatching(List<Integer>[] graph, int n2) {
		int n1 = graph.length;
		int[] dist = new int[n1];
		int[] matching = new int[n2];
		Arrays.fill(matching, -1);
		boolean[] used = new boolean[n1];
		for (int res = 0; ; ) {
			bfs(graph, used, matching, dist);
			boolean[] vis = new boolean[n1];
			int f = 0;
			for (int u = 0; u < n1; ++u)
				if (!used[u] && dfs(graph, vis, used, matching, dist, u))
					++f;
			if (f == 0)
				return res;
			res += f;
		}
	}

	static void bfs(List<Integer>[] graph, boolean[] used, int[] matching, int[] dist) {
		Arrays.fill(dist, -1);
		int n1 = graph.length;
		int[] Q = new int[graph.length];
		int sizeQ = 0;
		for (int u = 0; u < n1; ++u) {
			if (!used[u]) {
				Q[sizeQ++] = u;
				dist[u] = 0;
			}
		}
		for (int i = 0; i < sizeQ; i++) {
			int u1 = Q[i];
			for (int v : graph[u1]) {
				int u2 = matching[v];
				if (u2 >= 0 && dist[u2] < 0) {
					dist[u2] = dist[u1] + 1;
					Q[sizeQ++] = u2;
				}
			}
		}
	}

	static boolean dfs(List<Integer>[] graph, boolean[] vis, boolean[] used, int[] matching, int[] dist, int u1) {
		vis[u1] = true;
		for (int v : graph[u1]) {
			int u2 = matching[v];
			if (u2 < 0 || !vis[u2] && dist[u2] == dist[u1] + 1 && dfs(graph, vis, used, matching, dist, u2)) {
				matching[v] = u1;
				used[u1] = true;
				return true;
			}
		}
		return false;
	}

	// Usage example
	public static void main(String[] args) {
		List<Integer>[] graph = Stream.generate(ArrayList::new).limit(3).toArray(List[]::new);
		graph[0].add(0);
		graph[0].add(1);
		graph[1].add(1);
		System.out.println(2 == maxMatching(graph, 2));
	}
}